You can definitely play the game. It ran smoothly on my Surface Pro 2 (at least the first few dozen turns) and looks just as crisp as on my PC. But playing on the Surface sapped all the enjoyment I had for the game. The interface is too awkward (lots of right-clicking) that it's not enjoyable. I was constantly sending units to the wrong tile in both the main map and the battle map. IIRC, I also ended up having to zoom way in to have any accuracy which then resulted in making the experience feel really cramped as well.

Steam runs fine. And my experience with the Surface Pro 2 is that it can handle most of the indies on Steam. I would go ahead and install it and get it all set up and then see how it played for you.

And since you're going to be laid up, maybe you could just get a cheapo USB mouse? Or, splurge on a gamepad?

I have done neither thing (mostly because I use my Surface for work, not games). Having said that, my best gaming experiences on my surface have been playing older games (Railroad Tycoon 2 and Baldur's Gate) and using the stylus.